Two spherical bodies $\mathrm{A}$ (radius $6 \mathrm{~cm}$ ) and $\mathrm{B}$ (radius $18 \mathrm{~cm}$ ) are at temperature $\mathrm{T}_1$ and $\mathrm{T}_2$, respectively. The maximum intensity in the emission spectrum of $\mathrm{A}$ is at $500 \mathrm{~nm}$ and in that of $\mathrm{B}$ is at $1500 \mathrm{~nm}$. Considering them to be black bodies, what will be the ratio of the rate of total energy radiated by $A$ to that of $B$ ?
IIT 2010, Advanced
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$ \lambda_{\mathrm{m}} \mathrm{T}=\text { constant } $
$ \lambda_{\mathrm{A}} \mathrm{T}_{\mathrm{A}}=\lambda_{\mathrm{B}} \mathrm{T}_{\mathrm{B}}$
Rate of total energy radiated $\propto \mathrm{AT}^4$
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